IJCST Vol. 3, Issue 1, Jan. - March 2012
ISSN : 0976-8491 (Online) | ISSN : 2229-4333 (Print)
Speed Control of Separately Excited D.C Motor using Self
Tuned ANFIS Techniques
1
1,2
Sanju Saini, 2Arvind Kumar
Dept. of Electrical Engineering, Deenbandhu Chhotu Ram University of Science
& Technology, Murthal, Haryana, India
Abstract
This paper presents a comparison of performance of controllers
such as PI, PID controller, Self tuned fuzzy controller, G.A Fuzzy
PID & Self Tuned ANFIS, for DC motor speed control. Simulation
results have demonstrated that the use of Self Tuned ANFIS results
in a good dynamic behaviour of the DC motor, a perfect speed
tracking with no overshoot, gives better performance and high
robustness than those obtained by use of the other controllers.
Torque Constant, K = 3.475 Nm A-1
Armature winding resistance, Ra = 7.56 ohm
Armature winding inductance, La= 0.055 H
Friction coefficient (Bm) = 0.008 N.m/rad/sec
Sampling period, T = 40ms.
Keywords
DC Motor Speed Control, Fuzzy Controller, G.A & Neuro-Fuzzy
Controller
I. Introduction
With the development of power electronics resources, the direct
current machine has become more and more useful. The speed
of DC motor can be adjusted to a great extent as to provide
easy controllability and high performance. There are several
conventional as well as intelligent controllers to control the speed
of DC motor such as: PID Controller, Fuzzy Logic Controller,
G.A , Neuro-Fuzzy Controller etc. The Adaptive Neuro-Fuzzy
Inference System (ANFIS), developed in the early 90s by Jang,
combines the concepts of fuzzy logic and neural networks to form a
hybrid intelligent system that enhances the ability to automatically
learn and adapt. Hybrid systems have been used by researchers for
modeling and predictions in various engineering systems.
The basic idea behind these neuro-adaptive learning techniques
is to provide a method for the fuzzy modeling procedure to learn
information about a data set, in order to automatically compute
the membership function parameters that best allow the associated
FIS to track the given input/output data. The membership function
parameters are tuned using a combination of least squares
estimation and back-propagation algorithm for membership
function parameter estimation. These parameters associated with
the membership functions will change through the learning process
similar to that of a neural network. Their adjustment is facilitated
by a gradient vector, which provides a measure of how well the
FIS is modeling the input/output data for a given set of parameters.
Once the gradient vector is obtained, any of several optimization
routines could be applied in order to adjust the parameters so
as to reduce error between the actual and desired outputs. This
allows the fuzzy system to learn from the data it is modeling. The
approach has the advantage over the pure fuzzy paradigm that the
need for the human operator to tune the system by adjusting the
bounds of the membership functions is removed.
II. Mathematical Modeling & Controller Design
Motor to be controlled is a separately excited dc motor (as shown
in fig. 1.) with name plate ratings of 1 hp, 220V and 550 rpm.
Various parameters associated with the motor are:
Moment of Inertia of the motor rotor with attached mechanical
load,
J = 0.068 Kg-m2
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International Journal of Computer Science And Technology Fig. 1: Separately Excited Dc Motor
The armature voltage equation is given by:
Va = Eb+ Ia.Ra+ La. (dIa/dt)
(1)
For normal operation, the developed torque must be equal to the
load torque plus the friction and inertia, i.e.:
Tm = Jm. dω/dt +Bm .ω+TL
(2)
Where, TL is load torque in Nm.
III. Design of Controllers
A. PID Controller and Tuning
A feedback control system measures the output variable and sends
the control signal to the controller. The controller compares the
value of the output signal with a reference value and gives the
control signal to the final control element.
The equation of ideal PID controller is
The real PID controller is
The PID controller is traditionally suitable for second and lower
order systems. It can also be used for higher order plants with
dominant second order behaviour. The Ziegler-Nichols (Z-N)
methods rely on open-loop step response or closed-loop frequency
response tests. A PID controller is tuned according to a table
based on the process response test. According to Zeigler-Nichols
frequency response tuning criteria
Kp=0.6 kcu, τi =0.5T and τd =0.125T
For the PID controller used, the values of tuning parameters
obtained are
P= 18, I= 12, D=8.0.
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IJCST Vol. 3, Issue 1, Jan. - March 2012
ISSN : 0976-8491 (Online) | ISSN : 2229-4333 (Print)
B. Self Tuned Fuzzy Logic Controller
The Fuzzy controller developed here is a two-input single output
controller. The two inputs are the deviation from set point i.e. error,
e and error change rate, ∆e . The single output is the change of
actuating input, ∆u.
output. Membership functions used for input & output variables
are shown in fig. 4.
The membership functions of Gde sets are shown in fig. 4.
Table 1: Inference Rules for Main Fuzzy Logic
Fig. 4: Membership Function of Variables for Input Gain e, (a)
Error, (b). Change of Error, (c). Output
The structure of the rule base used for output gain can be visualized
from Table 3.
Table 3:
Fig. 2: Structure of Self-Tuning FLC
The membership functions of Ge sets are shown in fig. 3.
The membership functions of Gu sets are shown in fig. 5.
Fig. 3: Membership Function of Variables for Error .(a) Error (b)
Change of Error, (c). Output
Table 2: Inference Rules for Tuning the Input Gain Ge
To tune another input scaling factor Gde on the derivative
error side, the entries in Table 2 are considered in the opposite
manner, such as PB replaced by NB, PS replaced by NS and so
on, while constructing the fuzzy rule base. Here also, the two
input variables are the error and the derivative error but Gce is the
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Fig. 5: Membership Function of Variables, (a). Error, (b). Change
of Error, (c). Output
C. GA Tuned Fuzzy PID
GAs are powerful search optimization algorithms based on the
mechanism of natural selection and genetics. Gain of Fuzzy
PID are tuned using GA, which is implemented using matlab.
Typical values of different parameters of GAs are taken. The
programs use static values for maximum number of generations
(maxgen=100), probability of crossover (pc=0.8), and probability
of mutation(pm=0.05). The initial population is randomly
generated. The population size (psize=20), is selected based on the
observation. Roulette-wheel method is used to select individuals
for reproduction process. The selected strings undergo crossover
and mutation and become members of the new population. The
GA uses the absolute error i.e. the difference between the actual
output and the reference input as a fitness function.
International Journal of Computer Science And Technology 501
IJCST Vol. 3, Issue 1, Jan. - March 2012
ISSN : 0976-8491 (Online) | ISSN : 2229-4333 (Print)
D. Self Tuned Adaptive Neuro-Fuzzy Principle
The ANFIS is a multilayer feed-forward network which uses
neural network learning algorithms and fuzzy reasoning to map
inputs into an output. Indeed, it is a Fuzzy Inference System (FIS)
implemented in the framework of adaptive neural networks. For
simplicity, a typical ANFIS architecture with only two inputs
leading to four rules and one output for the first order Sugeno
fuzzy model is expressed. It is also assumed that each input
has two associated Membership Functions (MFs). It is evident
that this architecture can be easily generalized to our preferred
dimensions.
IV. Simulation Results
Simulink models of different controllers are developed &
simulated using MATLAB software. To test the robustness of
the different controllers, a reference speed of 20 rad/sec is chosen.
Fig. 6, represent the variation of motor speed w.r.t. time , while
using PI, PID controller, self tuned fuzzy controller, GA Tuned
fuzzy PID & Self tuned ANFIS respectively. Results shows that
ANFIS controller provides the best control minimizing overshoots
and settling time.
(a). PI
(d). GA TUNED FUZZY PID
(e). Self Tuned ANFIS
Fig. 6: The Speed Time Characteristic Obtained with the Help of
Different Controllers at a Reference Speed of 20 rad/sec, (a). PI
(b). PID (c). Self Tuned Fuzzy, (d). GA Tuned Fuzzy PID, (e).
Self Tuned ANFIS
Table 4 summarizes the results obtained with different
controllers.
Table 4: Performance With Different Controllers
502
(b). PID
(c). SELF TUNED FUZZY
International Journal of Computer Science And Technology It is clear that use of PI controller results in negligible steady state
error but overshoot and undershoot are quite large. In order to
improve the response, when Ziegler-Nichols tuned PID controller
is used, undershoot and overshoots are minimized. Use of adaptive
self tuned FLC helps to decrease settling time but steady state
error increases with no overshoots and undershoots. Hybrid
techniques such as GA tuned fuzzy PID controller further improve
the responses. Best results are obtained with self tuned ANFIS
controller, which results in minimum settling time with no steady
state error. Moreover, there are no overshoots and undershoots.
This controller gives the satisfactory performance even for variable
speed as shown in fig. 7.
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IJCST Vol. 3, Issue 1, Jan. - March 2012
ISSN : 0976-8491 (Online) | ISSN : 2229-4333 (Print)
(a). PI
(e). SELF TUNED ANFIS
Fig. 7: The speed time characteristics obtained with different
controllers with a change in reference speed from 20 to 25 rad/sec
at a time interval of 40 sec, (a). PI, (b). PID, (c). Self Tuned Fuzzy,
(d). GA TUNED Fuzzy PID, (e). Self Tuned ANFIS Controller.
It is clear from fig. 7, that proposed self tuned ANFIS controller
gives best response even when there is change in the reference
speed from 20 rad/sec to 25 rad/sec. Its use results in maximum
speed of response and minimum steady state error. It has the best
capability on tracking the reference signal.
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(b). PID
(c). SELF TUNED FUZZY
(d). GA TUNED FUZZY PID
V. Conclusion
In this paper, intelligent techniques such as Fuzzy logic Controllers
& their hybrid (ANFIS) are used for d.c. motor speed control. From
simulations, it is concluded that the use of ANFIS reduces design
efforts. Also, it results in minimum overshoots & undershoots &
increases the speed of response. Its response is even best under
variable reference speed which is shown from the results of second
set of simulations.
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Arvind Kumar M.Tech. student of
Instrumantation & Control in Electrical
Engg. department at Deenbandhu
Chottu Ram University of Science &
Technology, Murthal, Sonepat, Haryana,
India. Under the guidance of Asst. Proff.
Sanju Saini (DCRUST), Murthal. Arvind
Kumar received his B.TECH. Degree in
Instrumentation & Control in 2009 from
Haryana Engineering College, Haryana,
affiliated to Kurukshetra University. His research area is Use
of Intelligent Techniques. Woked as a lect in A.I.M.T (Aug
2011-Feb2012) Haryana. Presently working as lect. In Haryana
Engineering College (Haryana).
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